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From Mahjong Wiki, the mahjong encyclopedia

Initial Points

Because HKOS mahjong is also a gambling game, no initial points are specified. If you are playing casually everyone can start arbitrarily with 500 points.

Criteria

The hand must contain 14 tiles and be composed of four sets and a pair (with the exception of special limit hands). If two players call mahjong for the same discard, the player sitting closest to the discarder in turn order is given the tile. An exception to this is when a player completes a Thirteen Orphans hand the turn order does not matter.

Decide on a minimum number of fan needed before calling mahjong (3 fan is common). When declaring a win on a discard, the player must display his hand first before adding the discarded tile. In case of a self-drawn win, the drawn tile is displayed first followed by his hand.

Miss Win

Should a player fail to declare a winning tile, he/she cannot claim any identical discarded tile until his next draw.

Outline

If the winner wins by self-draw, then all other players pay him however much his hand is worth (or double its worth depending on the variation).

If the winner wins by discard, the player who discarded the winning tile (known as the discarder) is penalized. One common method of penalizing the discarder is forcing the discarder to pay the full value of the winning hand, while the other two players only pay half. Alternatively, the discarder must pay one or two times the value of the winning hand, while the other players pay nothing. Make sure your mahjong group agrees on a method of payment before starting a game.

Win by a discarded tile: Discarder pays winner double the full score.

Win by self-drawn tile: All player's pay double the full value of the winner's hand.

Scoring Table

Only the winning hand is scored. Determine which scoring elements apply to the winning hand then add. Use the table to convert the fan into points. However, different sources use different tables.